a book is opened. The product of the two page numbers is 600.
What are the two page numbers? Explain your thinking?
Take the square root of 600.
I'm sure you can figure out the two pages numbers from there.
You open the book to page 24 and 25. (They have to be consecutive integers like the pages in a book).
24*25=600.
To find the two page numbers, let's use a step-by-step approach.
Step 1: Define Variables
Let's assign variables to represent the page numbers. Let's call the left-hand page number x and the right-hand page number x+1.
Step 2: Set up the Equation
According to the problem, the product of the two page numbers is 600. So, we can write the equation as x(x+1) = 600.
Step 3: Solve the Equation
To solve the equation x(x+1) = 600, we can expand the equation and rewrite it as a quadratic equation:
x^2 + x - 600 = 0.
Step 4: Factor the Quadratic Equation
Let's factorize the quadratic equation:
(x-24)(x+25) = 0.
Step 5: Set Factors Equal to Zero
To find the values of x, we set each factor equal to zero:
x - 24 = 0 or x + 25 = 0.
Solving these equations, we get two possible solutions:
x = 24 or x = -25.
However, since we are dealing with page numbers, we cannot have a negative page number. So, we exclude x = -25 as a valid solution.
Step 6: Determine the Page Numbers
Since x = 24, we can substitute it back into our earlier definitions:
Left-hand page number = x = 24
Right-hand page number = x + 1 = 24 + 1 = 25.
Therefore, the two page numbers are 24 and 25.
To find the two page numbers in a book whose product is 600, we need to break down the problem into smaller steps.
Step 1: Understand the problem
We are given that a book is opened, but we don't know the specific page numbers. We are given that the product of the two page numbers is 600. Our task is to find the two page numbers.
Step 2: Set up the equation
Let's assume that the first page number is 'x' and the second page number is 'y'. Since we are looking for two numbers whose product is 600, we can set up the equation:
x * y = 600
Step 3: Factorize 600
To factorize 600, we need to find pairs of numbers whose product is 600. This can be done by splitting 600 into its prime factors. Here, the prime factors of 600 are 2, 2, 2, 3, 5, 5.
Step 4: Determine the pairs of numbers
Based on the prime factors, we can determine the pairs of numbers that multiply to give 600:
(1, 600)
(2, 300)
(3, 200)
(4, 150)
(5, 120)
(6, 100)
(8, 75)
(10, 60)
(12, 50)
(15, 40)
(20, 30)
(24, 25)
Step 5: Find the two page numbers
Looking at the pairs of numbers, we see that one of the pairs is (24, 25), which multiply to give 600.
Therefore, the two page numbers in the book are 24 and 25.